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lfunc_lfunctions • Show schema
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{'Lhash': '1438077319724737380905203856506', 'a10': [-0.6876415017203672, 0.0], 'a2': [0.0, 0.2334550310277294], 'a3': [-1.0, 0.0], 'a4': [1.9454987484878419, 0.0], 'a5': [0.0, 2.945498748487842], 'a6': [0.0, -0.2334550310277294], 'a7': [0.0, -1.0], 'a8': [0.0, 0.9210965327480967], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [3.3880065948035556, 1.2334550310277295]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.64', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2690562040898753948423038319945', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.2334550310277294], [-2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -2.945498748487842], [-5.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -3.621461625831285], [-11.0, 0]], [[1.0, 0], 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'4.69741478460604261659142356810736', '5.58414330373274965584556389888620', '6.65192502676089845684662448687840', '7.80809845386472579215069953802901', '8.933432722629424654857146771945235', '9.816896536178062028906560560626576', '11.21323758108477599505358190532573', '11.52202572924416195198343244873667'], 'prelabel': '2-273-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.38886221942999594, 'root_number': '0.34209887387303883 - 0.9396639614749512*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.194431109715', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13444297621586274594223265677', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89364023055856544602029483310', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69741478460604261659142356811', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '13.12', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/c/c/64/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-273-13.12-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-273-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.19443110971499797, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13444297621586274594223265677', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1438077319724737380905203856506', 'Lhash_array': ['1438077319724737380905203856506'], 'label': '2-273-13.12-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/c/c/64/5'}